The linear function is popular in economics. It is attractive because it is simple and easy to handle mathematically. It has many important applications. Linear functions are those whose graph is a ...

Linear graphs are straight-line graphs that visually represent a constant rate of change in the relationship between two variables, showing how one changes in response to the other. They are expressed ...

Derivative Graphs are visual representations of the derivative of a function with respect to its variable. They show how the slope of the tangent line to a curve changes at each point, allowing for an ...

This interactive figure allows the user to manipulate both the points and the line to observe the effects on the sum of residuals shown at the bottom of the figure. Modify Points: Checking this box ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(f(x) = x^2\) is the same as the graph of \(y = x^2\).

If \(f(x) = x^2\), then \(-f(x) = -(x^2)\). This means that each of the \(y\) coordinates will have a sign change. So \(y = 4\) would become \(y = -4\), and \(y = -1 ...